Current methods for defining SARS-CoV-2 lineages ignore the vast majority of the SARS-CoV-2 genome. We develop and apply an exhaustive vector comparison method that directly compares all known SARS-CoV-2 genome sequences to produce novel lineage classifications. We utilize data-driven models that (i) accurately capture the complex interactions across the set of all known SARS-CoV-2 genomes, (ii) scale to leadership-class computing systems, and (iii) enable tracking how such strains evolve geospatially over time. We show that during the height of the original Omicron surge, countries across Europe, Asia, and the Americas had a spatially asynchronous distribution of Omicron sub-strains. Moreover, neighboring countries were often dominated by either different clusters of the same variant or different variants altogether throughout the pandemic. Analyses of this kind may suggest a different pattern of epidemiological risk than was understood from conventional data, as well as produce actionable insights and transform our ability to prepare for and respond to current and future biological threats.